Hypercontractivity properties of nonsymmetric ornstein-uhlenbeck semigroups in hilbert spaces *

Author: Marco Fuhrman ^a

Affiliation:

^a Dipartimento di Matematica, Politecnico di Milano piazza Leonardo da Vinci, Milano, Italy

DOI: 10.1080/07362999808809531

Publication Frequency: 6 issues per year

Published in: journal

Stochastic Analysis and Applications, Volume 16, Issue 2 1998 , pages 241 - 260

Subjects: Statistics & Probability; Stochastic Models & Processes;

Formats available: PDF (English)

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Abstract

We prove hypercontractivity of nonsymmetric Ornstein-Uhlenbeck semigroups in Hilbert spaces, using direct probabilistic arguments. Our results imply exponential convergence at infinity for the semigroup. We show by examples that in our setting logarithmic Sobolev inequalities do not hold in general

^*Partally supported by Itlian MURST 60% research funds. Tis work was undertaken wile the author was Scuola Normale Superiore Pisa

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Hypercontractivity properties of nonsymmetric ornstein-uhlenbeck semigroups in hilbert spaces *

Abstract